Abstract
In this investigation, we use SAI method (Gupta et al. 2016), for solving sequencing problem when processing time of the machine is certain or uncertain in nature. The procedure adopted for solving the sequencing problems is easiest and involves the minimum numbers of iterations to obtain the sequence of jobs. The uncertainty in data is represented by triangular or trapezoidal fuzzy numbers. Yager’s ranking function approach is used to convert these fuzzy numbers into a crisp at a prescribed value of α. Stepwise SAI method is then used to obtain optimal job sequence for the problem. Further, the result obtained by SAI method is compared with Johnson’s Method. Numerical examples are given to demonstrate the effectiveness of the proposed approach.
Highlights
Sequencing problem is considered to be one of the classic and important applications of operations research
One of the renowned works in the field of sequencing considered till date is by Johnson (1954) who gave the algorithm for production scheduling in which he had minimized the total idle time of machines and the total production times of the jobs
Mukherjee &Basu (2010) used the ranking method to get the optimal assignment of jobs and Nirmala and Anju (2014) extend this method to get the optimal sequence of fuzzy sequencing problem
Summary
Sequencing problem is considered to be one of the classic and important applications of operations research. One of the renowned works in the field of sequencing considered till date is by Johnson (1954) who gave the algorithm for production scheduling in which he had minimized the total idle time of machines and the total production times of the jobs. While Kalczynski and Kamburowski (2006) were dealt with the classical problem of minimizing the makespan in a two-machine flow shop with deterministic job processing times, the optimal job sequence was determined by applying Johnson’s rule. Jain and Jain (2011) have presented Fuzzy TOPSIS method in job sequencing problems on machines of unequal efficiencies In this investigation, we consider a Job shop sequencing problem under certain and uncertain processing time.
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